ON THE WEIGHT HIERARCHY OF PREPARATA CODES OVER Z(4)

Abstract

Recently, Hammons et al. showed that, when properly defined, the binary nonlinear Preparata code can be considered as the Gray map of a linear code over Z(4), the so-called Preparata code over Z(4). In this paper, we consider the rth generalized Hamming weight d(r)(m) of the Preparata code of length 2(m) over Z(4). For any m greater than or equal to 3, d(r)(m) is exactly determined for r = 0.5, 1, 1.5, 2, 2.5, and 3.0. For a composite m, we give an upper bound on d(r)(m) using the lifting technique. For m = 3, 4, 5, 6, and 8, the weight hierarchy is completely determined. In the case of m = T, the weight hierarchy is completely determined except for d(4)(7).